If matrix $\begin{bmatrix$}[r] m - n & 8 \ 7 & m + n \end{bmatrix} = \text{matrix} \begin{bmatrix}[r] 2 & 8 \ 7 & 8 \end{bmatrix}, then the values of m and n are :

1. m = 2, n = 2

2. m = 5, n = 3

3. m = 3, n = 3

4. m = 3, n = 2

Given,

matrix $\begin{bmatrix$}[r] m - n & 8 \ 7 & m + n \end{bmatrix} = \text{matrix} \begin{bmatrix}[r] 2 & 8 \ 7 & 8 \end{bmatrix}

So,

1st equation :

⇒ m - n = 2

⇒ m = 2 + n ………(1)

2nd equation :

⇒ m + n = 8

Substituting value of m from (1) in above equation :

⇒ 2 + n + n = 8

⇒ 2n = 8 - 2

⇒ 2n = 6

⇒ n = $\dfrac{6}{2}$ = 3.

⇒ m = 2 + n = 2 + 3 = 5.

Hence, Option 2 is the correct option.